Ebook: Atomic and Molecular Nonlinear Optics: Theory, Experiment and Computation

A consistent scheme is proposed for quantizing the potential amplitude in the Schrödinger equation in the case of negative energies (lying in the discrete-spectrum domain). The properties of the eigenfunctions &phi;_ν(r) and eigenvalues α_ν corresponding to zero, small, and large absolute values of energy E < 0 are analyzed. Expansion in the set {&phi;_ν(r)} is used to develop a regular perturbation theory (for E < 0), and a general expression is found for the Green function associated with the time-independent Schrödinger equation. A similar method is used to solve several physical problems: the polarizability of a bound quantum-mechanical system, the two-center problem, and the elastic scattering of slow particles. The proposed approach is advantageous in that it does not require the use of continuum states (for E > 0).

A process of decomposition of fourth-rank tensors into parts irreducible with reference to the continuous group of rotation is presented. The transformation matrices between the Cartesian and spherical reducible and irreducible fourth-rank tensors are given and discussed. We have focused our attention to the purely dipolar fourth-rank tensor C_i;jkl symmetric to its last three indices and the dipole-octopole fourth-rank multipolar polarizability tensor E^(1,3). The fourth-rank tensors intervene in a number of very important nonlinear optics processes like Kerr effect, intensity-dependent refractive index phenomena, four wave mixing, third harmonic generation and several other effects. Tensors of this kind are also very important in piezo-electric phenomena and in elasticity studies. Cartesian tensor index permutation is discussed as well as its influence on the tensor irreducible spectrum is studied. Several examples concerning fourth-rank tensors are given.

In this work, we present the structural and the spectroscopic properties of the alkaline earth BeLi²⁺ ion for all the electronic states dissociating into Be⁺(2s, 2p, 3s, 3p, 3d, 4s, 4p, and 4d) + Li⁺ and Be²⁺ + Li (2s and 2p). We have used an ab initio approach involving a non-empirical pseudopoential for the Li⁺ and Be²⁺ cores and core-core and core-valence correlation corrections. For our best knoweledge, the adiabatic potential energy curves and the spectroscopic constants for nearly 18 electronic states of ²Σ⁺, ²Π and ²Δ symmetries are determined here for the first time. As neither experimental nor theoretical data are available for BeLi²⁺, our results are discussed and compared with similar systems such as BeH²⁺. Numerous avoided crossings between the electronic states of ²[loc=pre]Σ⁺ and ²Π symmetries have been localised and analysed. Their existences are related to the interaction between the potential energy curves and the charge transfer process between the two ionic systems Be⁽²⁺⁾Li and Be⁺Li⁺. Furthermore, we have calculated the adiabatic transition dipole moments from X²Σ⁺, 2²Σ⁺ and 3²Σ⁺ states to the higher electronic states of the same symmetry. This study represents the necessary initial step towards the investigation of the charge transfer processes in collision between Be⁺-Li⁺ and Be²⁺-Li.

Ab-initio finite field SCF calculations with split valence double zeta basis set indicate that 9, 10- donor-acceptor substituted anthracene derivatives have large quadratic hyperpolarizabilities for suitable combinations of donor and acceptor moieties. A difference in the first hyperpolarizabilities (β_total) of isomeric organic chromophores containing the same donor and acceptor groups indicate the possible role of intramolecular charge transfer (ICT) in shaping the NLO response in these π-conjugated molecular chromophores. A correlation is sought to be established among calculated (β_total) on one hand and the donor strength, the strength of the acceptor, donor-acceptor interaction and the donor-acceptor separation, on the other by using Genetic Algorithm (GA) to search through the relevant parameter space. It appears that (β_total) of a molecule is dominantly determined by additive contributions from the donors and the acceptors. The results might be helpful in designing new NLO materials using the bichromophoric anthracene derivatives.

The asymptotic model of exchange interactions for calculation of the polarizability of van der Waals complexes is discussed. The model is employed for description of the polarizability of interacting systems when their valence electron shells are weakly overlapped. The analytical expressions for the interaction polarizabilities that include induction, dispersion and exchange contributions have been obtained for X-Y and X-Y₂ complexes. The calculation of the interaction polarizabilities of the complexes He-He, Ar-Ar, Kr-Xe, Xe-Xe, and Ar-H₂ have been carried out.

Anomalous diffusion is considered in the context of fractional dynamics applied to dielectric relaxation of polyelectrolyte solutions. The approach starts from a fractional Smoluchowski equation in configuration space of molecular orientations of macroions and displacements of couterions. By using a perturbation procedure, we derive analytic expressions for the buildup and reversing field processes of the electric polarization given by the expectation value of the product of the first Legendre polynomial by the first Hermite polynomial. The first harmonic component of the ac dielectric response is also calculated. All these results are illustrated by plots demonstrating the effect of both the coupling (rotation-translation) parameter a and the critical exponent α (subdiffusion).

DFT and NMR calculations performed on isophlorin (1) and their derivatives (2–10) show that the 4O and the trans 2O, 2S derivatives (2 and 5) are anti-aromatic. The presence of strong S. . . S p_π-p_π bonding interactions stabilizes the planar structure (5) compared to the non-planar cis-isomer (8). Isophlorins are predicted to have very low electron reorganization energies (λ_electron ~ 0.10 eV) which remain unaffected by puckering through steric interactions or solvation in aqueous media. We predict isophlorins to be the ideal candidates for n-Channel organic conductors.

The modelling of the diethynylsilane derivatives reveals large magnitudes of the first hyperpolarizability (β). The electron donor (D) and acceptor (A) groups are attached at both ends of the oligomers that containing up to ten heterocyclic rings. Several D/A pairs with different strengths were tested in this investigation. The magnitude of static and dynamic β was computed using the AM1/TDHF methodology. The presence of the alkyl donor groups containing heteroatom in the oligomers investigated contributes most for the largest values of the β hyperpolarizability observed. The effect of the oligomer chain length on the β magnitude is also investigated. The results demonstrate that the diethynylsilane derivatives are promising as second-order nonlinear optical materials.

The process of Sum Frequency Generation (SFG) in chiral Carbon Nanotubes (CNTs), with the exciting laser beams propagating along the CNT symmetry axis, is here investigated. First the general form of the first hyperpolarizability third rank tensor β for chiral CNTs is determined with group projector technique method applied to the Ln_p22 line group describing their symmetry. For this purpose, the group natural factorization has been adopted and the associated irreducible representations, parameterized in terms of helical quantum numbers, then used to construct the group projector operator in the relevant vector space. The method demonstrates that second harmonic generation is symmetry forbidden in the collinear geometry while, conversely, SFG is symmetry allowed. Subsequently, the SFG far-field radiation pattern has been modelled with a calculation scheme derived from antenna's theory and already used for simulation of Rayleigh scattering from a CNT. The method has been overhauled for describing the here considered nonlinear optical interaction. The study of the role played by two induced counter-propagating current density retarded waves in shaping the radiation pattern is addressed and simulations are reported in the limit regimes of strong and weak attenuation.

In this paper, basis sets for H, C, N and O atoms were adjusted to obtain electric properties of diatomic molecules. The dipole moment, polarizability and first-order hyperpolarizability were calculated for H₂, CH⁺, CN^- and CO molecules and the basis sets modified to reproduce the reference data available. A sequential methodology was used, where the basis set for H is firstly adjusted and then used to fit the basis set for C in the CH⁺ molecule and so on. The final basis sets were (7s2p1d)→[3s2p1d] for H and (9s5p2d)→[5s3p2d] for C and O. In the case of N atom, the best basis set was found to be (9s5p1d)→[5s3p1d], where only one set of d polarization functions was needed. The atomic basis sets fitted were further utilized for calculation of geometry and electric properties of 36 benzene derivatives mono- and di-substituted by electron donor and acceptor groups attached at ortho, meta and para positions. The results were satisfactory for most of molecules. For instance, in the case of p-nitroaniline, an important push-pull benzene derivative, the first hyperpolarizability was predicted to be 9.4 × 10^-30 e.s.u. in excellent agreement with experimental value, 9.2 × 10^-30 e.s.u. Besides electric properties, our basis sets also gave good geometries for polyatomic molecules at reasonable computational cost. Therefore, the results reported in the present paper suggest the use of our modified basis sets for calculation of geometry and electric properties (linear and non-linear) of push-pull benzene derivatives like molecules.

The contribution of the quadrupole polarizability C to the long-range polarizability of two interacting rare-gas atoms and methane molecules is specified by fitting the trace and anisotropy models to the intensity of the isotropic and anisotropic interaction-induced light scattering spectra. Good agreement with ab initio results in the literature is obtained and the first few even moments of these profiles are in excellent agreement with experiments.

We discuss a simple model for creation of entanglement in a system composed of two two-level atoms interacting with a common environment. The role of the environment in entangling and disentangling of the atoms is explored. We demonstrate how the spontaneous decay of an initial excitation of the system can create a transient entanglement between the atoms. The opposite situation is also discussed where a spontaneous disentanglement of initially entangled atoms may exhibit some unusual features such as entanglement sudden birth, the phenomenon of entanglement sudden death and revival of entanglement. We provide a discussion of these unusual phenomena in terms of the density matrix elements of the system and show the connection of the phenomena with the threshold behaviour of the concurrence.

We here discuss a problem of time-resolved fluorescence polarization spectroscopy at two-photon excitations of macroscopically isotropic molecular media, that can be organized locally on a nano-scale. The simplifying assumptions on the hydrodynamical shape of fluorophores and on the form of the two-photon absorption tensor, are considered and displayed on the corresponding examples of the emission anisotropy synthetic decays. These assumptions reduce the number of the model parameters making the theoretical description of the discussed spectroscopic technique applicable in the experimental practice. Because the two-photon excitations of fluorescence require the application of the exciting light of appropriately high intensity, and that may have a negative influence on the quality of the experimental data collected, we discuss the application of the wide-angular detection-aperture technique in such experiments. Furthermore, we consider the application of the symmetry adapted callibration (SAC) method enabling one to accurately analyze the experimental data even if the collecting optics employed is not ideal and is affected by several unexpected technical imperfections that are hard to be accounted for analytically.

The absorption and scattering of IR radiation by aqueous ultradisperse systems that absorb nitrogen, oxygen, or argon are studied with the molecular dynamics method on the basis of a flexible molecule model. After nitrogen or argon is captured by an aqueous disperse system, the absorption of the IR radiation by this system increases owing to the enhancement of intramolecular vibrations. It is demonstrated that the integral intensity of absorption of IR radiation decays after water clusters adsorb oxygen. As the nitrogen concentration in a system of water clusters rises, the power of IR radiation emitted by the system increases significantly. The attachment of molecular oxygen by clusters leads to decay of the power of their IR radiation, while the capture of atomic oxygen, on the contrary, is accompanied by an increase in the rate of dissipation of energy accumulated by water aggregates. The power of radiation generated by cluster systems at the expense of thermal energy increases considerably when there is one adsorbed argon atom per cluster and decreases with a twofold increase in the number of argon atoms in clusters.

Assuming the low molecular reorientation approximation, the formulae for linear electric polarization induced in liquids composed of rigid, noninteracting, dipolar and asymmetric-top molecules in spherical solvents were derived. The Kalmykov's equation [Phys.Rev., E 65 (021101) 2001] – equivalent to the classical, noninertial Smoluchowski-Debye model of rotational diffusion was applied. In order to highlight the influence of the anisotropy of rotational diffusion tensor components and the orientation of permanent dipole moment of the molecule on the complex linear electric susceptibility, we present three-dimensional plots of the dispersion and absorption spectra, Cole-Cole diagrams for different values of the anisotropies of rotational diffusion tensor components and different frequencies of an ac electric field.

Recently, a novel type of intermolecular covalent interaction has been found in dimers with π-radical(s). In this paper, the optimized structure of the tetrathiafulvalence radical-cation dimer (TTF·⁺–TTF·⁺) is obtained with all-real frequencies, in which a 20-center-2-electron intermolecular covalent π/π bonding with a double-tube shape is theoretically predicted. The covalent π/π bonding energy is estimated to be about -21 kcal·mol^-1 which counteracts partly the Coulombic repulsion between two TTF·⁺ cations. This intermolecular covalent bonding can also influence the structure of the TTF·⁺ subunit, i.e., its molecular plane is bent by an angle &theta; = 5.6°. In addition, adding the background charges based on the TTF-TCNQ crystal structure, the interaction energy of TTF·⁺–TTF·⁺ changes from a positive value to a large negative value.

This work indicates that the TTF-TCNQ crystal structure built up from parallel, segregated stacks of cation radicals TTF·⁺ and anions TCNQ·^- is stabilized by two main factors: the intermolecular covalent π/π bonding interaction between like-charged radicals and the effect of counterions.

In earlier work, Li, Ahuja, Harrison, and Hunt have calculated the collision-induced polarizability Δα of a pair of hydrogen molecules at CCSD(T) level with an aug-cc-pV5Z basis, for 178 relative orientations of the pair, with the bond length in each molecule fixed at r = 1.449 a.u. Here we present new results from an expansion of the second-rank tensor components of Δα as series in the spherical harmonics of the molecular orientation angles and the orientation angles of the intermolecular vector. The coefficients in this expansion depend on the separation R between the molecules. We compare the ab initio coefficients with predictions from long-range perturbation theory, including the dipole-induced-dipole interactions at first and second order, higher-multipole induction, effects of nonuniform local fields, hyperpolarization, and van der Waals dispersion. Li and Hunt have derived equations for the long-range coefficients complete to order R^-6, using spherical-tensor methods developed by Bancewicz, Głaz, and Kielich for collision-induced light scattering by centrosymmetric linear molecules. We also give new results here for the van der Waals dispersion terms in both isotropic and anisotropic polarizability coefficients. We have calculated these coefficients by 64-point Gauss-Legendre quadrature, using the H₂ polarizabilities and hyperpolarizabilities at imaginary frequencies computed by Bishop and Pipin, with explicitly correlated wave functions for isolated H₂ molecules. We show that the ab initio values for the larger anisotropic polarizability coefficients converge to the predictions of the long-range theory, as the separation R between the molecules increases. The coefficients computed ab initio have been used by Gustafsson, Frommhold, Li, and Hunt to calculate the depolarized collision-induced roto-translational Raman spectra of hydrogen gas at 36 K and 50 K out to 800 cm^-1, and at 296 K out to 300 cm^-1. The general features of the experimental spectra are well reproduced, although the calculated intensities are ~30% too large over much of the frequency range.

Some of the experimental measurements of the frequency shift and phase-conjugation fidelity gained from previous studies of stimulated scattering (SS) of nanosecond (5 ÷ 10 ns) near-ultraviolet (uv) (λ = 193 ÷ 351 nm) laser pulses in liquids (hexane, heptane, and others) are found to disagree with the theory of SS, which takes into account only the linear (single-photon) light absorption. To resolve the inconsistency, SS of XeCl excimer laser radiation (λ = 308 nm) with the duration of 8 ns in liquid hexane is investigated experimentally. A theoretical analysis of the results obtained revealed three nonlinear optical phenomena induced by the heating due to two-photon absorption: stimulated thermal scattering (two-photon STS-2), phase mismatch for stimulated Brillouin scattering (SBS), and phase self-modulation. The experimental SS spectrum contains two additional lines – a two-photon STS-2 line and a genuine SBS line in the near-uv region.

The effects of linear (single-photon) and two-photon heating to the thin structures of the stokes and anti-stokes spectral components of stimulated Brillouin scattering (SBS) and stimulated temperature scattering (STS) are compared. The thin structures of the linear and two-photon STS-2 possess the same shapes. For the Fabry-Perot etalon based spectrum analyzer the linear and two-photon STS-2 components are experimentally indistinguishable not only from one another, but also from the STS-1 component. To reach the higher spectral resolution methods of heterodyning and intensity fluctuations correlation should be used. In contrast to a linear (single-photon) case for two-photon heating a stokes SBS component exhibits the spectral shift depending on the pump intensity. Emergence of the anti-stokes SBS component is possible when the pump intensity is sufficiently high so that the positive two-photon thermal gain may compensate the negative electrostrictive gain.